The frequency with which a surfactant monomer enters and leaves a surfactant micelle has been the subject of much discussion. It is possible, using EPR, to measure the frequency with which a paramagnetic molecule changes to a magnetically different environment if that frequency is between 105 and 109 sec-1, or alternatively to state whether the exchange frequency is faster or slower than these limits. If the paramagnetic molecule were also a surfactant, this technique would give information about the exchange frequency between monomer and micelle, since these have magnetically different environments. A series of paramagnetic surfactants (I) was prepared. The EPR spectra of micellar solutions of these surfactants consisted of one broad line due to the micelles, superimposed upon three sharp lines due to the monomeric nitroxide surfactant. This showed that the monomer- micelle exchange frequency was in the slow region. Increasing the temperature increased the width of the monomer lines, and it was initially thought that this was indicative of measurable monomer-micelle exchange. Further experiments produced inconsistent results. In an attempt to understand these results, a theoretical investigation of the linewidth behaviour expected for monomer-aggregate exchange was made, which indicated that under certain conditions the mI = +1 nitroxide lines might broaden more than the mI = 0 line. This would enable one to distinguish monomer-aggregate exchange from Heisenberg spin exchange. Since these linewidth effects were small, an attempt was made, by computer-simulation, to take into account the effect of proton hyperfine structure on the observed linewidth. This attempt was not successful as the proton hyperfine coupling constants were found to decrease with increasing exchange frequency in the region of interest. The problem was further complicated by the presence of pre-micellar aggregates, which seem to be caused by the nitroxide head group and not by the hydrocarbon chains of the surfactant. A final series of experiments showed that the observed linewidth increases were not due to monomer-micelle exchange, but to a combination of monomer-dimer exchange and Heisenberg spin exchange. Thus this EPR technique yields only the information that the monomer-micelle exchange frequency is slower than 105 sec-1. Other EPR experiments involving the nitroxide analogue of an oily soil are described. The physical state of the paramagnetic soil on fabric, the removal of the soil under different conditions, and the re-deposition of the soil are described, as is the construction of a capillary washing chamber, an effective washing-machine simulator which operates in the cavity of an EPR spectrometer and in which these experiments were performed.